Cook pasta according to package directions. Drain.
In a 3-quart saucepan, melt butter until sizzling. Stir in flour, salt, and pepper. Add whole milk. Cook over medium heat, stirring constantly, until mixture boils and thickens, or about 5 to 7 minutes. Reduce heat to low and stir in cheese. Stirring constantly, warm cheese until it is melted, or about 5 to 7 minutes.
Once cheese is melted, add cooked pasta and coat well. Mix in lobster meat, making sure to incorporate the chunks evenly. Add additional pepper to taste.
Remove from heat and serve topped with bacon crumbles and fresh chives.
*Consuming raw or undercooked meats, poultry, seafood, shellfish, or eggs may increase your risk of foodborne illness.